That's the whole point of a cold wallet 😂 The key is on an external, non internet connected device. You use that to sign the transaction, then transfer the signed transaction back to an internet connected device to broadcast to the blockchain.
Discussion
But why do I need a device to do that? If I just have the key, I can sign.
You don't need one, but it is probably more secure. A key stored on your computer or phone can be more vulnerable to theft, hacking, malware, etc.
